Related papers: Bayesian autoregressive spectral estimation
Using a proper model to characterize a time series is crucial in making accurate predictions. In this work we use time-varying autoregressive process (TVAR) to describe non-stationary time series and model it as a mixture of multiple stable…
Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure,…
The approximation of a stationary time-series by finite order autoregressive (AR) and moving averages (MA) is a problem that occurs in many applications. In this paper we study asymptotic behavior of the spectral density of finite order…
We consider a class of vector autoregressive models with banded coefficient matrices. The setting represents a type of sparse structure for high-dimensional time series, though the implied autocovariance matrices are not banded. The…
This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in…
We consider a prior for nonparametric Bayesian estimation which uses finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
We study the problem of robust time series analysis under the standard auto-regressive (AR) time series model in the presence of arbitrary outliers. We devise an efficient hard thresholding based algorithm which can obtain a consistent…
In this paper I present a new approach for regression of time series using their own samples. This is a celebrated problem known as Auto-Regression. Dealing with outlier or missed samples in a time series makes the problem of estimation…
We present a probabilistic autoencoder (PAE) framework for galaxy spectral energy distribution (SED) modeling and redshift estimation, applied to synthetic SPHEREx 102-band spectrophotometry. Our PAE learns a compact latent representation…
Purpose: Undersampling is used to reduce the scan time for high-resolution 3D magnetic resonance imaging. In order to achieve better image quality and avoid manual parameter tuning, we propose a probabilistic Bayesian approach to recover…
Autoregressive (AR) models have become a popular tool for unsupervised learning, achieving state-of-the-art log likelihood estimates. We investigate the use of AR models as density estimators in two settings -- as a learning signal for…
Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…
Estimating the periodicity of a stationary time series via fitting a second order stationary autoregressive (AR(2)) model has been initiated by the seminal paper of Yule(1927).. We investigate properties of this procedure when applied to a…
This paper presents an innovative extension of spatial autoregressive (SAR) models, introducing spatial coefficients specific to each spatial region that evolve over time. The proposed estimation methodology covers both homoscedastic and…
In this work, we consider the class of multi-state autoregressive processes that can be used to model non-stationary time-series of interest. In order to capture different autoregressive (AR) states underlying an observed time series, it is…
The Rayleigh regression model was recently proposed for modeling amplitude values of synthetic aperture radar (SAR) image pixels. However, inferences from such model are based on the maximum likelihood estimators, which can be biased for…
Change detection is an important synthetic aperture radar (SAR) application, usually used to detect changes on the ground scene measurements in different moments in time. Traditionally, change detection algorithm (CDA) is mainly designed…
Spatial autoregressive model, introduced by Clif and Ord in 1970s has been widely applied in many areas of science and econometrics such as regional economics, public finance, political sciences, agricultural economics, environmental…